We have measured the hyperfine structure splittings of the three components of the ${2p}^{4}3s{}^2{P}_J\to {2p}^{4}3p{}^2{D}_{J^{\prime }}$ multiplet in atomic fluorine using both Doppler-free saturated absorption spectroscopy with an external cavity diode laser and Doppler-limited absorption spectroscopy with a noncavity diode laser. Specifically, we have obtained spectra of the $J=1/2\mathrm{}\to J^{\prime }=3/2\mathrm{}$ transition 780 nm, the $J=3/2\mathrm{}\to J^{\prime }=5/2\mathrm{}$ transition at 775 nm, and the $J=3/2\mathrm{}\to J^{\prime }=3/2\mathrm{}$ transition at 761 nm. The fluorine atoms were generated from a 10% mix of ${\mathrm{F}}_2$ in He using a 2.45-GHz microwave generator and cavity pressures of approximately 0.5 torr. We report here values for hyperfine splittings and constants for the upper and lower states of these transitions. In addition, the absolute frequency of one of the hyperfine components of the $J=1/2\mathrm{}\to J^{\prime }=3/2\mathrm{}$ transition at 780 nm was measured using a recent absolute frequency measurement of the $D_2$ transition in Rb.

A recently developed extension to a three-dimensional finite-element Schrödinger equation solver in the total angular momentum representation was used to calculate the energy-level spectrum and wave functions for antiprotonic helium system. The accuracy of the numerical method was analyzed. Relativistic and QED corrections to the energy levels were calculated in the main order. Excellent agreement was reached between relativistically corrected wavelengths and recent experimental data. Radiative transition probabilities and lifetimes were calculated and compared with other calculations as well as with experiment.

A discrete variable representation (DVR) appropriate for describing the highly excited states of hydrogen atoms in laboratory-strength magnetic fields is constructed by using a symmetry-adapted direct product of one-dimensional DVR’s in parabolic coordinates related to generalized Gauss-Laguerre quadratures. The resulting sparse Hamiltonian matrix is used in an iterative (filter-diagonalization) procedure to obtain eigenvalues and eigenvectors in a given spectral domain. The method is applied to calculate eigenvalues and lifetimes of “circular” Rydberg states, as well as oscillator strengths for the excitation of highly excited states.

Measurements are reported for the lifetimes of the $6p{}^2{P}_{1/2,3/2},$ $6d{}^2{D}_{3/2,5/2},$ $7s{}^2{S}_{1/2},$ $7p{}^2{P}_{1/2,3/2},$ $7d{}^2{D}_{5/2},$ and $5f{}^2{F}_{5/2,7/2}$ levels in Tl III, made using beam-foil excitation. Theoretical calculations are also presented to elucidate conditions of configuration interaction exhibited by the measurements. In addition, values for the measured $6p$ lifetimes in the Au sequence are combined with theoretical calculations of resonance transitions to higher levels to specify the ground-state dipole polarizabilities for Au I, Hg II, Tl III, Pb IV, and Bi V.

In this paper we develop a theoretical framework for studying spin polarization of one or both of the two electrons emitted in the one-photon, one-step, double ionization of an atom. The expressions derived herein are in the form of an incoherent sum over the angular momentum $j_t$ exchanged between the unobserved initial and final angular momenta. It then naturally facilitates an analysis of spin-resolved double-photoionization processes in terms of the parity-favored and -unfavored transitions. Several photon-propagation and electron-detection configurations are considered in which it becomes simpler to study the angular-spin or spin-spin correlation between two photoelectrons. The approach suggested in this paper has been used to analyze spin-resolved double photoionization in the ${6s}^2$ subshell of atomic ytterbium.

Electron capture in ${\mathrm{H}}^{+}+\mathrm{S}{(}^3{P,}^{1}D)$ collisions is studied theoretically by using a semiclassical molecular representation with five molecular channels from the initial ground and excited states at collision energies above 10 eV. Electron capture in ${\mathrm{S}}^{+}$ ${(}^{4}S)+\mathrm{H}(1\mathrm{}\mathrm{}\mathrm{s})$ collisions is also investigated by using three molecular channels in order to assess the earlier estimation which gave the rate constant of ${10}^{-15}{\mathrm{cm}}^3/\mathrm{s}$ at ${10}^4\mathrm{K}$ for the process. The ab initio potential curves and nonadiabatic coupling matrix elements for the ${\mathrm{HS}}^{+}$ system are obtained from multireference single- and double-excitation configuration-interaction calculations employing relatively large basis sets. Dominant capture channels corresponding to the $\left[{\mathrm{H}+\mathrm{S}}^{+}{(}^{2}P\right)]$ and $\left[{\mathrm{H}+\mathrm{S}}^{+}{(}^{2}D\right)]$ states lie lower by 0.2 and 1.4 eV, and 1.34 and 2.5 eV from the initial ground $[{\mathrm{H}}^{+}+\mathrm{S}{(}^{3}P)]$ and excited $[{\mathrm{H}}^{+}+\mathrm{S}{(}^{1}D)]$ states, respectively. The present results show that electron capture from the excited species is found to be rather weak at lower energies. But it rapidly becomes comparable to that from the ground state. Electron capture in ${\mathrm{S}}^{+}$ ${(}^{4}S)+\mathrm{H}$ collisions proceeds through the two-step mechanism at lower energies, and therefore, the cross section is found to be small with the value less than ${10}^{-17}{\mathrm{cm}}^2$ below 1 keV, thus supporting the earlier estimation.

The multiconfiguration Hartree-Fock method for continuum wave functions has been used to perform calculations of elastic scattering of electrons from the open-shell sulfur atom at low energies. The electron correlation and polarization of the sulfur atom by the scattered electron, which are very important in this calculation, have been taken into account very accurately ab initio through the configuration-interaction procedure by optimizing both bound and continuum orbitals simultaneously at each kinetic energy of the scattered electron. The scattering lengths, phase shifts, and differential, total and momentum-transfer cross sections for electrons elastically scattered from sulfur atoms are calculated for the impact-energy range from 0 to 27.2 eV. The wave functions computed exactly at zero energy are used to compute the scattering length. The present results are compared with other available theoretical results.

$L$ x-ray emission from Xe ions incident on a variety of solid targets at energies ranging from 6 to 15 MeV/u has been investigated using a curved crystal spectrometer of moderate resolution. Analysis of the spectra provided estimates of the average charges and (in some cases) the charge distributions of those ions emitting $L$ x rays inside the targets. Calculations employing theoretical electron capture and loss cross sections were used to examine the dependence on depth within the target of contributions to the spectra from Xe ions having different average numbers of $L$ and $M$ electrons. Average charges and charge distributions deduced from the x-ray spectra were found to agree quite well with those predicted by the model calculations.

Final product states of ${\mathrm{Ne}}_2^{+}$ dissociative recombination were studied using time-of-flight spectroscopy to determine the kinetic energies released. The dissociative recombination occurred in a sustained discharge in the presence of a variable magnetic field and discharge voltage, at pressures of 5–15 mTorr. Under different conditions various excited states were observed ranging from the lowest $3s$ metastable states to higher Rydberg states within 0.000 54 eV of the dissociation limit. From their narrow widths, it is deduced that these higher states arose from ${\mathrm{Ne}}_2^{+}$ ions with subthermal energies. From two of these narrow distributions, we obtain an improved value for the dissociation limit $D_0{(\mathrm{N}\mathrm{e}}_2^{+})=1.26\mathrm{}\pm 0.02\mathrm{}\mathrm{eV}.$

In the widely used Hartree-Fock procedure for atomic structure calculations, trial functions in the form of linear combinations of Slater determinants are constructed and the Rayleigh-Ritz minimum principle is applied to determine the best in that class. A generalization of this approach, applicable to low-energy electron-atom scattering, is developed here. The method is based on a unique decomposition of the scattering wave function into open- and closed-channel components, so chosen that an approximation to the closed-channel component may be obtained by adopting it as a trial function in a minimum principle, whose rigor can be maintained even when the target wave functions are imprecisely known. Given a closed-channel trial function, the full scattering function may be determined from the solution of an effective one-body Schrödinger equation. Alternatively, in a generalized Hartree-Fock approach, the minimum principle leads to coupled integrodifferential equations to be satisfied by the basis functions appearing in a Slater-determinant representation of the closed-channel wave function; it also provides a procedure for optimizing the choice of nonlinear parameters in a variational determination of these basis functions. Inclusion of additional Slater determinants in the closed-channel trial function allows for systematic improvement of that function, as well as the calculated scattering parameters, with the possibility of spurious singularities avoided. Electron-electron correlations can be important in accounting for long-range forces and resonances. These correlation effects can be included explicitly by suitable choice of one component of the closed-channel wave function; the remaining component may then be determined by the generalized Hartree-Fock procedure. As a simple test, the method is applied to $s$-wave scattering of positrons by hydrogen.

The kinetic-energy distribution of $\mathrm{D}\mathrm{}\left(2p\right)\mathrm{}$ atoms resulting from electron-impact dissociation of ${\mathrm{D}}_2$ has been measured. A high-resolution vacuum ultraviolet spectrometer was employed for the first measurement of the D Lyman-α (D $L\alpha$) emission line profiles at 20- and 100-eV excitation energies. Analysis of the deconvoluted line profile of D $L\alpha$ at 100 eV reveals the existence of a narrow line central peak of $29\pm 2\mathrm{m}\AA$ full width at half maximum and a broad pedestal wing structure about 190 mÅ wide. The wings of the line can be used to determine the fast atom distribution. The wings of D $L\alpha$ arise from dissociative excitation of a series of doubly excited states that cross the Franck-Condon region between 23 and 40 eV. The fast atom distribution at 100-eV electron impact energy spans the energy range from 1 to 10 eV with a peak value near 6 eV. Slow $\mathrm{D}\mathrm{}\left(2p\right)\mathrm{}$ atoms characterized by a distribution function with peak energy near 100 meV produce the central peak profile, which is nearly independent of the impact energy. The deconvoluted line profiles of the central peak at 20 eV for dissociative excitation of ${\mathrm{D}}_2$ and ${\mathrm{H}}_2$ are fitted with an analytical function for use in calibration of space flight instrumentation equipped with a D/H absorption cell. The kinetic-energy and line profile results are compared to similar measurements for ${\mathrm{H}}_2.$ The absolute cross sections for the line center (slow atoms) and wings (fast atoms) and total emission line profile were measured from threshold to 400 eV. Analytical model coefficients are given for the energy dependence of the measured slow atom cross section.

A two-dimensional analog of Levinson’s theorem for nonrelativistic quantum mechanics is established, which relates the phase shift at threshold (zero momentum) for the $m$th partial wave to the total number of bound states with angular momentum $mħ$ $(m=0,1,2,\dots )$ in an attractive central field.

Absolute cross sections for dissociative attachment of electrons to the ground and electronically excited states have been measured using the relative flow technique. The excited molecules were prepared by laser optical pumping and their fraction was determined from the reduction in the dissociative attachment signal from the ground state. The cross sections for the excited state were determined by normalizing to this fraction. The success of this experiment should lead to similar measurements on other molecules.

Absolute cross sections for single- and double-electron capture, and single-electron loss, have been determined for ${\mathrm{O}}^{7,8+}$ ions colliding with Ar and Ne in the energy range 8–40 MeV. Double-electron-capture cross sections were found to be factors of 5–10 smaller than the single-electron capture cross sections. The present results for electron capture from Ar are systematically larger by about 30% than the corresponding cross sections determined previously by Macdonald and Martin [Phys. Rev. A 4, 1965 (1971)]. The present single-electron-capture cross sections agree well with the empirical scaling rule of Schlachter et al. [Phys. Rev. A 27, 3372 (1983)].

We propose a general approach to the electron-impact ionization problem that involves two distinct steps. First, using exterior complex scaling, we calculate the outgoing portion of the scattering wave function without explicit use of boundary conditions for ionization or any other channel. Once that wave function is known for a finite region of space, we make use of a general formula for extracting the integral cross section for the breakup process from any wave function. That formula is a projected form of the optical theorem and has no relation to complex coordinates or other methods of computing the scattering wave function. A preliminary calculation on the $s$-wave radial limit form of electron–hydrogen-atom ionization is presented in excellent agreement with calculations by other approaches.

Muon catalyzed fusion in deuterium traditionally has been studied in gaseous and liquid targets. The TRIUMF solid-hydrogen-layer target system has been used to study the fusion reaction rates in the solid phase of D${}_2$ at a target temperature of 3 K. Products of two distinct branches of the reaction were observed: neutrons by a liquid organic scintillator and protons by a silicon detector located inside the target system. The effective molecular formation rate from the upper hyperfine state of $\mu d$ and the hyperfine transition rate have been measured: ${\tilde{\lambda }}_{\frac{3}{2}}{=2.71\mathrm{}\left(7\right)\mathrm{}}_{\mathrm{stat}}{\mathrm{}\left(32\right)\mathrm{}}_{\mathrm{syst}}\mu {\mathrm{s}}^{-1}$ and ${\tilde{\lambda }}_{\frac{3}{2}\frac{1}{2}}{=34.2\mathrm{}\left(8\right)\mathrm{}}_{\mathrm{stat}}{\mathrm{}\left(1\right)\mathrm{}}_{\mathrm{syst}}\mu {\mathrm{s}}^{-1}$. The molecular formation rate is consistent with other recent measurements, but not with the theory for isolated molecules. The discrepancy may be due to incomplete thermalization, an effect that was investigated by Monte Carlo calculations. Information on branching ratio parameters for the $s$ and $p$ wave $d+d$ nuclear interaction has been extracted.

The process of electron-impact ionization of atoms, normally called $\mathrm{}(e,2e)\mathrm{}$, has been studied for three decades. Most of this work has concentrated on energies far from autoionization resonances. However, for electron energies corresponding to an autoionization resonance, it is not possible to distinguish electrons that have been ejected directly from the atom from those that were first excited to an autoionizing level and subsequently ejected. As a result, these two processes will interfere and the interference can potentially be sensitive to different physical effects from the normal $\mathrm{}(e,2e)\mathrm{}$ process far from resonances. In this paper, we will examine $\mathrm{}(e,2e)\mathrm{}$ for cadmium in the energy range of autoionizing levels. First-order distorted-wave results will be compared with recent measurements.

Resonant transfer excitation (RTE) involving $L^{-1}\mathrm{Mn}$ $(n>~M)$ resonant states has been investigated for Na-like and Ne-like ${\mathrm{Cu}}^{q+}+{\mathrm{H}}_2$ collisions $(q=18\mathrm{}$ and 19). The $M$- to $L$-shell x-ray production cross sections (RTEX’s) of these resonance states are studied by x-ray projectile ion coincidences. Previous measurements of $L$-shell RTEX for ${\mathrm{Nb}}^{q+}$ $(q=28\mathrm{}–31)$ ions showed the measured cross sections to be nearly a factor of 2 smaller than the calculated ones. For ${\mathrm{Cu}}^{18+}$ the present results show the position and width of the measured RTEX maximum cross section to be in agreement with the calculations; however, the measured absolute cross sections are about 60% higher than the predicted ones. In the case of Ne-like ${\mathrm{Cu}}^{19+}$ projectiles, the metastable component in the beam made it impossible to observe RTEX’s.

The electron-impact ionization cross section of ${\mathrm{Be}}^{+}$ is calculated using both a time-dependent and a time-independent close-coupling method. The time-dependent method is based on the propagation of wave packets constructed using excited-state orbitals calculated in a core pseudopotential. The time-independent method is an $R-$matrix solution based on a total wave function constructed using antisymmetrized products of Laguerre pseudo-orbitals and zero-derivative box orbitals. In both methods, low partial-wave close-coupling results are added to high partial-wave distorted-wave results to yield ionization cross sections for ${\mathrm{Be}}^{+}$ substantially below the experimental crossed-beam measurements of Falk and Dunn [Phys. Rev. A 27, 754 (1983)] and in agreement with the recent time-independent close-coupling calculations of Bartschat and Bray [J. Phys. B 30, L109 (1997)].

Velocity-space pictures of the electron continua produced by the impact of ions on He and Ne have been measured for the bare projectiles of $p,$ He, C, O, and Ne at a projectile velocity of 1.63 a.u. For the three highly charged projectiles, this velocity lies in the ionization “threshold” region where electron capture dominates the reaction. The electron velocity-space distributions for these cases are concentrated near the velocity of the projectile, not near the saddle-point velocity, and seem to “saturate” at a nearly universal shape. The data are in qualitative agreement with CDW-EIS calculations.